Lessons on Structure from the Structure of Viruses

As the most primitive organisms, occupying the gray area between the living and nonliving, viruses are the least complex biological systems. We make some observations about their structure, formalizing in mathematical terms some rules-of-construction discovered by Caspar and Klug. We call the resulting structures “objective structures”. It is seen that objective structures include many important structures studied in science today: carbon nanotubes, the capsids, necks, tails of many viruses, the cilia of some bacteria, buckyballs, actin and collagen and many common proteins, and typical nano-rods/springs/wires now being synthesized by methods of self-assembly. This common mathematical structure paves the way toward many interesting calculations for such structures: simplified schemes for exact calculations of energy and dynamics of such structures (objective DFT/MD), new x-ray methods for direct determination of structure not relying on crystallization, and a theory of their growth.